Name **_____________________** I.D. Number

Unit 5 Evaluation 419 MTHH 041

Unit 5 Evaluation

Evaluation 05

Introduction to Statistics

(MTHH 041 055)

This evaluation will cover the lessons in this unit. It is open book, meaning you can use your

textbook, syllabus, and other course materials. You will need to understand, analyze, and apply the

information you have learned in order to answer the questions correctly. To submit the evaluation,

follow the directions provided.

Multiple-Choice

Select the response that best completes the statement or answers the question.

Use this information to answer questions 1 – 5.

Oceanographers believe that 28% of coral in a large reef have a fungus. A survey team will

inspect 142 different locations on the reef.

q

ˆ .

a. 0.72

b. 0.20

c. 0.28

d. 0.80

3. Find the standard deviation of the proportion.

a. 0.280

b. 0.0377

c. 0.720

d. 0.80

mean?

a. (0.28, 0.3554)

b. (0.2046, 0.3177)

c. (0.2423, 0.3177)

d. (0.2046, 0.3554)

Unit 5 Evaluation 420 MTHH 041

a. Yes, since it is inside the confidence interval.

b. Yes, since it is outside the confidence interval.

c. No, since it is inside the confidence interval.

d. No, since it is outside the confidence interval.

Use this information to answer questions 6 – 8

A chicken hatchery claims that 80% of their eggs successfully hatch. A farmer purchases 60

eggs from the hatchery to start his own flock.

a. 0.20

b. 0.95

c. 0.80

d. 0.60

a. 60 chicks

b. 80 chicks

c. 48 chicks

d. 75 chicks

a. 0.0516

b. 0.1032

c. 0.80

d. 0.0067

Unit 5 Evaluation 421 MTHH 041

Barack Obama was born outside the country. Based on those results, we’ve

simulated several samples of 50 people. This histogram displays the proportion of

people who answered yes to this question in each of those samples. What does the

striped bar represent?

a. The striped bar represents a 95% confidence interval between 0.20 and 0.25 that

the President was born outside the country.

b. The striped bar represents a Normal model, N(0.20, 0.25).

c. The striped bar represents 47 samples where between 20 and 25 percent believed

the President was born outside the country.

d. The striped bar represents between 0.20 and 0.25 of the 50 people believe that the

President was born outside the country.

Use this information to answer questions 10 – 11.

A regular die is tossed 60 times and the proportion of rolls that are 1 or 2 is recorded. This is

repeated many times.

a.

1

3

; 0.0609

b.

1

3

; 0.0430

c.

2

3

; 0.0609

d.

2

3

; 0.0430

Unit 5 Evaluation 422 MTHH 041

change if we were to roll the die fewer times.

a. Mean would stay the same; standard deviation would decrease.

b. Mean would stay the same; standard deviation would increase.

c. Mean would decrease; standard deviation would increase.

d. Mean would decrease; standard deviation would stay the same.

35% of voters surveyed believe increasing taxes for those making more than $250,000

would be good for the economy. The margin of error was ±3%. What can you conclude

about all American voters?

a. We can be reasonably certain that the true percentage of American voters who

believe increasing taxes for those making more than $250,000 is between 29%

and 41% (±2 standard deviations).

b. We can be reasonably certain that the true percentage of American voters who

believe increasing taxes for those making more than $250,000 is between 32%

and 38%.

c. We can be reasonably certain that 35% of those surveyed make between $80,000

and $95,000.

d. We can be reasonably certain that all American voters believe that taxes should be

increased for those making more than $250,000.

Reports, 40% say they have chosen not to fill a prescription because it cost too much.

Find the 95% confidence interval.

a. (0.3845, 0.4155)

b. (0.5845, 0.6155)

c. (0.3696, 0.4304)

d. (0.559, 0.631)

president is doing. Which best describes a sampling distribution of the sample

proportion in this situation?

a. A confidence interval containing the true proportion of voters who approve of the

president.

b. The proportion of these 3,500 voters who approve the president.

c. The proportion of all voters who approve the president.

d. The proportions who approve the president within all possible samples of this size.

a. There is a 95% probability that the true proportion is this interval.

b. The interval contains 95% of the true proportion.

c. 95% of the time, the sample proportion and the true proportion will be the same.

d. 95% of intervals constructed this way will contain the true proportion.

Unit 5 Evaluation 423 MTHH 041

distribution of proportions?

a. We must expect more than 10 successes and more than 10 failures.

b.

npq

c.

ˆ ˆ ( )ˆ

pq SE p

n

d. The outcomes within each sample are not independent.

a. Using a non-random sample does not affect the accuracy of a confidence interval.

b. Our method requires that the sample size must be less than 10% of the population

we are investigating.

c. The value of p depends on our sample.

d. The data values can be dependent on each other.

adults in one city, 8 were unemployed. Which is true?

a. p = 0.16 and

p

ˆ

= 0.13

b. The 95% confidence interval for this city’s jobless rate is 0.044 to 0.235.

c. The sample size is not large enough to use a Normal model for the sampling

distribution.

d. This situation does not meet the 10% Condition for using a Normal model to model

the sampling distribution.

express disapproval of his job performance. His political committee pays for a series

of TV ads, hoping that they can lower negatives to below 30%. The pollsters test the

hypothesis that the ads produced no change against the alternative that the negatives

are now below 30% and find a P-value of 0.22. Which conclusion is correct?

a. There’s a 22% chance that the ads worked.

b. There’s a 78% chance that the ads worked.

c. There’s a 22% chance that their poll is correct.

d. There’s a 22% chance that natural sampling variation could produce poll results like

these if there is really no change in public opinion.

Unit 5 Evaluation 424 MTHH 041

been drinking during the 30 days preceding their survey. A state youth council

believes this proportion is lower in their state where there had been an intense media

campaign against riding with drivers who have been drinking. A survey of randomly

chose students from across the state shows 304 of 1214 students answering yes to

this question. What are the hypotheses in this survey?

a. H0: p = 0.29; HA: p < 0.29 b. H0: p = 0.29; HA: p > 0.29

c. H0: p = 0.71; HA: p > 0.71

d. H0: p = 0.71; HA: p < 0.71

b. H0: p = 0.80; HA: p > 0.80

c. H0: p > 0.80; HA: p = 0.80

d. H0: p = 0.80; HA: p < 0.80 30. Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts(H0: p = 0.97 and HA: p > 0.97). The

test results in a P-value of 0.122. Unknown to the manufacturer, the machine is

actually producing 99% good parts. What probably happens as a result of the testing?

a. They correctly fail to reject H0.

b. They fail to reject H0, making a Type I error.

c. They fail to reject H0, making a Type II error.

d. They reject H0, making a Type I error.

31. A report on health care in the US said that 28% of Americans have experienced times

when they haven’t been able to afford medical care. A news organization randomly

sampled 801 black Americans, of whom 304 reported that there had been times in the

last year when they had not been able to afford medical care. Assuming that this test

meets the criteria for assumptions and conditions, what would be the z-score?

a. 6.27

b. 0.3795

c. 0.0995

d. 1.96

32. The step of hypothesis testing that tests the assumptions and conditions is called what?

a. Conclusion

b. Hypotheses

c. Mechanics

d. Model

Unit 5 Evaluation 427 MTHH 041

33. In 2005 the U.S. Census Bureau reported that 68.9% of American families owned their

homes. Census data reveal that the ownership rate in one small city is much lower.

The city council is debating a plan to offer tax breaks to first-time home buyers in order

to encourage people to become homeowners. They decide to adopt the plan on a 2-

year trial basis and use the data they collect to make a decision regarding tax breaks.

Since this plan costs the city tax revenue, they will continue to us it only if there is

strong evidence that the rate of home ownership is increasing. What would be the

effect of a Type II error?

a. The city concludes that home ownership is on the rise.

b. The city foregoes tax revenue.

c. The city withdraws help from those who might otherwise have been able to buy a

house.

d. The city continues to lose money.

34. The seller of a loaded die claims that it will favor the outcome 6. We don’t believe that

claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns

out to be 0.03. Which conclusion is appropriate? Explain

a. There’s a 3% chance that a loaded die could randomly produce the results we

observed so it’s reasonable to conclude that the die is fair.

b. There’s a 3% chance that a fair die could randomly produce the results we

observed, so it’s reasonable to conclude that the die is loaded.

c. There’s a 3% chance that the die is fair.

d. There’s a 97% chance that the die is fair.

35. A company with a fleet of 150 cars found that the emissions systems of 7 out of 22 they

tested failed to meet pollution control guidelines. Is this strong evidence that more

than 20% of the fleet may be out of compliance? Which conditions/assumptions are

not met in order to use the Normal model?

i. Independence assumption

ii. Randomization Condition

iii. 10% Condition

iv. Success/Failure Condition

a. ii and iv

b. i and iii

c. ii and iii

d. iii and iv

36. As the value of α gets smaller, how does this affect the z-score?

a. The z-score of a one-tailed test is higher.

b. The z-score for a one-tailed test is lower.

c. The z-score for a two-tailed test is lower.

d. There is no change in the z-score.

Unit 5 Evaluation 428 MTHH 041

__

month. The mean wait was 47.7 minutes with a standard deviation of 33.14 minutes.

Describe the center, and spread in context of the sampling distribution of means of

random samples of 75 calls taken from this population.

a. mean: 47.7 minutes; standard deviation: 33.14 minutes

b. mean: 74 df; standard deviation: 3.83 minutes

c. mean: 47.7 minutes; standard deviation: 3.83 minutes

d. mean: 74 df; standard deviation: 33.14 minutes** _ 38. A government report on housing costs says that single-family home prices nationwide are skewed to the right, with a mean of $235,700. We collect price data from a random sample of 50 homes in Orange County, California. Why is it okay to use these data for inference even though the population is skewed? a. We can then say the degrees of freedom are 49. b. As the sample size increases, the distribution of sample means will be a t-model. c. We are talking about the sampling distribution of prices which always follows a Normal model. d. We can find the mean and the standard deviation. 39. A hypothesis test of whether the mean number of hours adults spend on their cell** 50. A

phones is more than 30 minutes per day produces a P-value of 0.112. Explain what

this means in context.

a. We would expect about 11.2% of samples of the same size to have a distribution as

high or higher than the one we saw in our sample.

b. We would expect about 11.2% of samples of the same size to have a sample mean

as high or higher than the one we saw in our sample.

c. 11.2% of our sample population spent more than 30 minutes per day on their cell

phones.

d. The mean length of time that adults spent on their cell phones was more than 30

minutes 11.2% of the time.

Unit 5 Evaluation 429 MTHH 041

40. How does the t-model compare to the Normal model for various sample sizes?

a. As the sample size decreases, the t-model comes closer to approximating a Normal

model.

b. The larger sample sizes increase the variation so the t-model and Normal model

become more similar.

c. As the sample size increases, the t-model comes closer to approximating a Normal

model.

d. The difference between the two is the degrees of freedom.

41. It is expected that a quarter of the responses to the question “Do you enjoy being a

parent?” will be “unsure” and there will be twice as many “yes” as “no” responses. Find

the expected distribution for 86 responses.

a. Yes: 0.5; No: 0.25; Not Sure: 0.25

b. Yes: 42; No: 22; Not Sure: 22

c. Yes: 50%; No: 25%; Not Sure: 25%

d. Yes: 43; No: 21.5; Not Sure: 21.5

Use the following information to answer questions 42 – 44.

Here are the weights in ounces of a random sample of 25 oranges harvested at Sunny Day

Orchards this season.

12.6 10.0 11.4 13.6 12.8

8.0 9.7 10.1 9.5 7.1

9.0 9.3 6.5 15.9 7.4

14.1 5.1 8.8 4.9 8.1

10.8 7.5 4.6 10.1 10.2

42. Find the standard error for this sample.

a. 0.5641

b. 0.9843

c. 0.5455

d. 0.5758

43. What is the margin of error?

a. 1.1885

b. 2.0316

c. 1.1643

d. 1.126

Unit 5 Evaluation 430 MTHH 041

44. Find the 95% confidence interval.

a. (8.2956, 10,673)

b. (7.4524, 11.5156)

c. (8.3197, 10.6483)

d. (8.358, 10.61)

45. Interpret the confidence interval (7.569, 9.325) for another sample from Blue Stem

Orchards, a neighboring orchard.

a. 95% of all oranges from Blue Stem Orchards weigh between 7.569 ounces and

9.325 ounces.

b. I am 95% confident that the mean weight of an orange from Blue Stem Orchards

this season is between 7.569 ounces and 9.325 ounces.

c. I am 95% confident that a randomly selected orange from Blue Stem Orchards this

season is between 7.569 ounces and 9.325 ounces.

d. 95% of all samples from Blue Stem Orchards will have mean weight between 7.569

ounces and 9.325 ounces.

46. The distribution of salaries of television news broadcasters is skewed to the right. Which

is true according to the Central Limit Theorem?

a. The distribution of all the salaries of the broadcasters can be described by a Normal

model.

b. The spread of the sampling distribution of sample means would be smaller for small

samples than for larger samples.

c. The sampling distribution of means for large random samples of these salaries can

be approximated by a Normal model.

d. The standard deviation of the sampling distribution of means for large random

samples of these salaries is equal to

pqˆˆ

n

.

Use this information to answer questions 47 – 49.

A group of teenagers is chosen randomly and asked which of three indoor activities they

preferred. Of the 126 teenagers, 36 preferred listening to music, 16 preferred reading, and

the rest preferred going online or playing video games. You are wondering if these

responses indicate a preference among teenagers in general.

47. Find the actual count and the expected count for each activity.

a. Music:36, 0.286; Reading: 16, 0.127; Online/Gaming: 74, 0.587

b. Music:36, 42; Reading: 16, 42; Online/Gaming: 74, 42

c. Music:42, 36; Reading: 42, 16; Online/Gaming: 42, 74

d. Music:36, 126; Reading: 16, 126; Online/Gaming: 74, 126

Unit 5 Evaluation 431 MTHH 041

48. Find the

2

statistic.

a. 0.857

b. 24.381

c. 41.333

d. 2 degrees of freedom

49. Assuming a very small P-value for the

2

statistic, what conclusions can be drawn?

a. There is strong evidence that there is a difference in teenagers’ preference among

these three indoor activities.

b. There is strong evidence that there is no difference in teenagers’ preference among

these three indoor activities.

c. The probability that this is accurate is very small.

d. A very small proportion of teenagers were sampled.

__

2

statistic is calculated to be 37.12. What should you conclude?

a. Reject the null hypothesis.

b. Fail to reject the null hypothesis.

c. The standard deviation is most cases will be less than 37.12.

d. Not enough information is given.

Carefully check your answers on this evaluation and make any corrections you feel are

necessary. When you are satisfied that you have answered the questions to the best of your

ability, transfer your answers to an answer sheet. Please refer to the information sheet that

came with your course materials.

Sample Solution

Socialism is a conviction that everybody in the public eye ought to be equivalent and offer their riches. This is the result of communism and sanctification (Laskin 45). After the Russian unrest in 1917, it turned into a strong wellspring of data. As per Karl Marx, "All as per his capacity, as per his needs" these speculations are scattered by Mr. Karl Marx. He accepts that putting forth himself mirrors his attempts (McLellan 1). He additionally accepts that socialism or uniformity is "the last phase of life" (Leone 1). "Network" is an indistinct term on the off chance that it is utilized equivalently with "gathering". People are individuals from numerous gatherings and are hence part of numerous networks. School is a network. The people group is a network. The city is a network. The expert is a network. The congregation is a network. Accordingly, schools are a) networks, b) elements in bigger networks, and c) littler networks. That implies excessively, the network has neither rhyme nor reason. Schools examine well about their associations with the network. This shows the school is not the same as the network. To be sure, schools exist in covering networks and can go about as networks themselves. The people group is a gathering of individuals who are identified with one another and share normal qualities. Geology is neither a network, a part nor a fortuitous event. A gathering of individuals in a network with a typical point (eg history, values, unwaveringness, shared objectives). In this structure, network individuals are given enrollments (eg "comparative") characterized by individuals' possession dependent on outside definition measures identified with network capacities (eg as school of understudies) and individual trust for participation Recognition) is incorporated. Individuals with political or social issues 2 Citizenship is the way that the regular association among individuals is more prominent than that of enormous families (counting relatives), and resident's dynamic, cooperation, administration and It is the rule of authoritative administration. , Mechanism and Process The expression "network" is frequently used to allude to where individuals live and to all individuals living there. A people group may likewise allude to a gathering of individuals who perceive themselves as networks since encounters, life stories, values, religion, culture, and so forth are shared. The chairman can consider his town a network, however in many urban areas there are a few self-characterized networks - the Italian-American people group, the gay network, the Jewish people group, the African American people group, the business network I don't accept that all individuals from these networks have a similar view or act a similar way, yet I think there is something in the same way as different individuals from the network.>

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